Let EC denote the complexified adjoint Lie-algebra bundle associated to P . For the purposes of this summary, we will assume that E = EC; the more general case will be dealt with in section 7. Let dt : Ω (M ;EC)→Ω (M ;EC) denote the exterior derivative corresponding to At for each t. At t = 0, we wish to calculate the dimension of ker(D0), which gives the number of eigenvalues λα(t) of Dt passi...

Let M̃ be a (2m+ 1)-dimensional almost contact manifold with almost contact structure (φ,ξ,η), that is, a global vector field ξ, a (1,1) tensor field φ, and a 1-form η on M̃ such that φ2X =−X +η(X)ξ, η(ξ) = 1 for any vector field X on M̃. We consider a product manifold M̃×R, whereR denotes a real line. Then a vector field on M̃×R is given by (X , f (d/dt)), where X is a vector field tangent to M̃, t ...

In this paper, primal-dual methods for general nonconvex nonlinear optimization problems are considered. The proposed methods are exterior point type methods that permit primal variables to violate inequality constraints during the iterations. The methods are based on the exact penalty type transformation of inequality constraints and use a smooth approximation of the problem to form primal-dua...

We consider the problem of sweeping (or grazing) the inte-rior/exterior of a polygon by a exible rope whose one end point (anchor) is attached on the boundary of the polygon. We present a linear time algorithm to compute the grazing area inside a simple polygon. We show how to extend the algorithm for computing the internal grazing area, without increasing its time complexity, to compute the gr...

A set without tangents in PG(2, q) is a set of points S such that no line meets S in exactly one point. An exterior set of a conic C is a set of points E such that all secant lines of E are external lines of C. In this paper, we first recall some known examples of sets without tangents and describe them in terms of determined directions of an affine pointset. We show that the smallest sets with...

In this paper we present a theoretical investigation and an extensive computational study of Exterior Point Simplex Algorithm (EPSA) initialization methods for the Assignment Problem (AP). We describe the exterior point algorithm using three different initialization methods. Effective implementations are explored for each initialization method. Then we perform an experimental evaluation on a la...

In math.GT/0510607, a conjecture is suggested by J. Dubois and R. Kashaev. It is that the differential coefficient of the abelian Reidemeister torsion of a knot exterior at a bifurcation point of the SL(2, C)-representation variety of its knot group corresponds a limit value of the non-abelian twisted Reidemeister torsion of the knot exterior. We shall prove this conjecture in the present paper.

We consider the defocusing energy-critical NLS in the exterior of the unit ball in three dimensions. For the initial value problem with Dirichlet boundary condition we prove global well-posedness and scattering with large radial initial data in the Sobolev space Ḣ1 0 . We also point out that the same strategy can be used to treat the energy-supercritical NLS in the exterior of balls with Dirich...